A proclamation seems unlikely to do that, though it does touch a series of issues:

My Administration has partnered with the LGBT community to advance a wide range of initiatives. At the international level, I have joined efforts at the United Nations to decriminalize homosexuality around the world. Here at home, I continue to support measures to bring the full spectrum of equal rights to LGBT Americans. These measures include enhancing hate crimes laws, supporting civil unions and Federal rights for LGBT couples, outlawing discrimination in the workplace, ensuring adoption rights, and ending the existing "Don't Ask, Don't Tell" policy in a way that strengthens our Armed Forces and our national security. We must also commit ourselves to fighting the HIV/AIDS epidemic by both reducing the number of HIV infections and providing care and support services to people living with HIV/AIDS across the United States.

Full proclamation after the jump.

For Immediate Release June 1, 2009
LESBIAN, GAY, BISEXUAL, AND TRANSGENDER PRIDE MONTH, 2009
- - - - - - -
BY THE PRESIDENT OF THE UNITED STATES OF AMERICA
A PROCLAMATION
Forty years ago, patrons and supporters of the Stonewall Inn in New York City resisted police harassment that had become all too common for members of the lesbian, gay, bisexual, and transgender (LGBT) community. Out of this resistance, the LGBT rights movement in America was born. During LGBT Pride Month, we commemorate the events of June 1969 and commit to achieving equal justice under law for LGBT Americans.
LGBT Americans have made, and continue to make, great and lasting contributions that continue to strengthen the fabric of American society. There are many well-respected LGBT leaders in all professional fields, including the arts and business communities. LGBT Americans also mobilized the Nation to respond to the domestic HIV/AIDS epidemic and have played a vital role in broadening this country's response to the HIV pandemic.
Due in no small part to the determination and dedication of the LGBT rights movement, more LGBT Americans are living their lives openly today than ever before. I am proud to be the first President to appoint openly LGBT candidates to Senate-confirmed positions in the first 100 days of an Administration. These individuals embody the best qualities we seek in public servants, and across my Administration -- in both the White House and the Federal agencies -- openly LGBT employees are doing their jobs with distinction and professionalism.
The LGBT rights movement has achieved great progress, but there is more work to be done. LGBT youth should feel safe to learn without the fear of harassment, and LGBT families and seniors should be allowed to live their lives with dignity and respect.
My Administration has partnered with the LGBT community to advance a wide range of initiatives. At the international level, I have joined efforts at the United Nations to decriminalize homosexuality around the world. Here at home, I continue to support measures to bring the full spectrum of equal rights to LGBT Americans. These measures include enhancing hate crimes laws, supporting civil unions and Federal rights for LGBT couples, outlawing discrimination in the
more
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workplace, ensuring adoption rights, and ending the existing "Don't Ask, Don't Tell" policy in a way that strengthens our Armed Forces and our national security. We must also commit ourselves to fighting the HIV/AIDS epidemic by both reducing the number of HIV infections and providing care and support services to people living with HIV/AIDS across the United States.
These issues affect not only the LGBT community, but also our entire Nation. As long as the promise of equality for all remains unfulfilled, all Americans are affected. If we can work together to advance the principles upon which our Nation was founded, every American will benefit. During LGBT Pride Month, I call upon the LGBT community, the Congress, and the American people to work together to promote equal rights for all, regardless of sexual orientation or gender identity.
NOW, THEREFORE, I, BARACK OBAMA, President of the United States of America, by virtue of the authority vested in me by the Constitution and laws of the United States, do hereby proclaim June 2009 as Lesbian, Gay, Bisexual, and Transgender Pride Month. I call upon the people of the United States to turn back discrimination and prejudice everywhere it exists.
IN WITNESS WHEREOF, I have hereunto set my hand this
first day of June, in the year of our Lord two thousand nine, and of the Independence of the United States of America the two hundred and thirty-third.
BARACK OBAMA
# # #

Maybe I'm suspicious, but... does 'ending the existing "Don't Ask, Don't Tell" policy' necessarily mean "allowing gay, out people to serve in the military"?
After all, gays couldn't serve in 1992, before DADT was implemented. He could end that policy--and replace it with another policy that also, explicitly or implicitly, kept gays from serving--and say that he had, indeed, ended "Don't Ask, Don't Tell".

It's about time! What kind of democracy can our nation boast if it forces patriotic service people who are gay to lie under oath? For Dan Choi to be dismissed when he has been serving this nation so patriotically, how can we even dare to claim that "We support our Troops." It will only go to say that we are a nation of hypocrites!
STOP THE FIRING OF DAN CHOI, PRESIDENT OBAMA. When we claim that we support the Troops, we ought to be supporting Dan Choi, too.

Lifting the ban would mean institutional sexual harassment. There is no privacy in the Army. I remember standing in lines for open showers, doubling room occupancy. It the same way that you cannot demand female soldiers to room with male soldiers or shower with them, you cannot demand it when one person is gay.
You will have the same problems if you put men and women together. There is a reason why the military prohibts gays in the military and relationships between men and women in the same units. It's not morality, it necessary to maintain discipline.

Other militaries manage to pull it off. The whole sexual harrassment argument centers on the silly myth that a gay soldier can't hang out with straight soldiers without getting turned on. It's simple. Any soldier, male or female, who sexual harrasses another soldier, male or female, gets disciplined. Repeat or serious offenders end up in the stockade.

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This is contray to Muslim teaching and will not stand around the world. You can get away with it in San Francisco, but the world follows moral teachings of the prophet. Obama needs to mind his own business.

Homosexual actions remain punishable under the Uniform Code of Military Justice. Congress would have to amend the law. Ironically, for those arguing for ending the existing "Dont ask, don't tell" executive order, homosexual behavior can be openly investigated.

Below is a copy of a comment I sent to the OBAMA White House. I know he could just STOP this harassment until Congress acts. I think BC was wrong to listen to the brass in sign this in to a low law.We now must go the next step and outlaw discrimination by the United States of America Government and military.
"In the copy of the Press briefing which Mr Gibbs tried to explain the OBAMA's thinking about the DADT DOD. In saying that a legislative solution is the correct way and I agree with that BUT there is NO way the PRESIDENT can't STOP the harassment of gay AMERICAN CITIZENS who work for the UNITED STATES of AMERICA by not only canning them but ruin there life. Come on if the past President did this by feat you sure can just STOP the harassment.
Thank You wit loVe J Rome
" MR Gibbs: What I talked about in terms of "don?t ask, don?t tell" was the President...,supports changing that because he strongly believes that it does not serve our national interest. ....the only durable solution to "don?t ask, don?t tell" is through a legislative process, and the President is working.....to ensure that that happens.
Q But couldn?t he in the meantime put a moratorium on these discharges until that can be accomplished?
Mr.Gibbs: ..the President has determined that...that?s not the way to seek any sort of lasting or durable solution
Q Then how would you respond to the criticism, though, that dismissing a qualified linguist endangers the troops?
MR. GIBBS: I think I would respond by saying that the President has long believed that the policy doesn?t serve our national interest. "